General Guidelines

Candidates for PhD degrees at Stanford must satisfactorily complete a program of study that includes 135 units of graduate course work and research. At least 3 units must be taken with each of four different Stanford faculty members. Study lists are submitted quarterly through Student AXESS with a total 10 units of coursework. Graduate students (including MD/PhD students in the graduate student phase of their training) must take all required courses for a letter grade. The university requires that you maintain a 3.0 GPA in order to remain enrolled at Stanford University.

In addition to courses, students must also complete at least three lab rotations, pass qualifying exams, and participate in other program requirements before they earn their PhD.  Details on these additional requirements and the program training timeline may be found below.

• IMMUNOL 200: Cellular and Molecular Immunology: An Introductory Course (MI 200, BIO 230)
  Mechanisms of immune responses in health and disease. Innate and adaptive immunity; development of the immune system; molecular biology, structure, and function of antibodies and T-cell receptors; cellular basis and regulation of immune responses; infectious diseases and vaccines; allergy, inflammation, and autoimmunity. COVID-19 will be featured as a major example. Lectures and discussion in class and in sections. For upper class undergraduate and graduate students who have not had an introductory immunology course. Prerequisites for undergraduates: Biology Core, Human Biology Core, or BIO 83 and 86, or consent of instructor. For graduate students: College-level molecular biology, biochemistry, and cell biology, or consent of instructor.
  
  Terms:  Autumn | Units:  4

• All students in the two tracks, Molecular, Cellular, and Translational Immunology (MCTI) and Computational and Systems Immunology (CSI) are required to enroll in the following core courses:

  BIOS 200: Foundations in Experimental Biology
  This course is divided into two 3-week cycles. During the first cycle, students will be developing a 2-page original research proposal, which may be used for NSF or other fellowship applications. In the second cycle, students will work in small teams and will be mentored by faculty to develop an original research project for oral presentation. Skills emphasized include: 1) reading for breadth and depth; 2) developing compelling, creative arguments; 3) communicating with the spoken and written word; 4) working in teams. Important features of the course include peer assessment, interactive joint classes, and substantial face-to-face discussion with faculty drawn from across the Biosciences programs. Shortened autumn quarter class; class meets during weeks 1 through 8 of the quarter.
  
  Terms: Autumn | Units: 5
• BIOS 217:    Foundations of Statistics and Reproducible Research
  Introduction to foundations of rigorous, reproducible research in experimental biology and clinical research. Provides conceptual framework for linking hypotheses to experimental design, quantitative measurement, statistical analysis and assessment of uncertainty. Course combines lecture presentation and discussion of core concepts from statistics and reproducibility with hands-on exposure to best practices for reproducible workflows spanning design, data collection, annotation, analysis and presentation of results. Brief discussion of social, legal, and ethical issues with reproducibility in scientific practice, along with NIH grant requirements. Course provides foundations for future learning in these areas. Examples drawn from multiple areas of experimental biology and clinical research. Target audience: Students in BIOS 200 (Foundations in Experimental Biology), in Biosciences graduate programs or T32 training programs. Prerequisites: None
  
  Terms: Autumn | Units: 2
  
• BIO 141: Biostatistics (STATS 141)
  Statistical methods for biological and medical applications. Collecting data (random sampling, randomized experiments); describing data (numerical and graphical summaries); probability models; statistical inference (hypothesis tests and confidence intervals). Use of software to conduct probability simulations and data analysis. This is an introductory course; students with previous experience in statistics should consider taking STATS 191 instead.
  
  Terms: Autumn | Units: 5
  • Or EPI 258: Introduction to Probability and Statistics for Clinical Research
    Open to medical and graduate students; required of medical students in the Clinical Research Scholarly Concentration. Tools to evaluate medical literature. Topics include random variables, expectation, variance, probability distributions, the central limit theorem, sampling theory, hypothesis testing, confidence intervals, correlation, regression, analysis of variance, and survival analysis.
    
    Terms: Spring | Units: 3
  • Or EPI 259: Introduction to Probability and Statistics for Epidemiology
    (HUMBIO students must enroll in EPI 159. Med/Graduate students must enroll in EPI 259.) Topics: random variables, expectation, variance, probability distributions, the central limit theorem, sampling theory, hypothesis testing, confidence intervals. Correlation, regression, analysis of variance, and nonparametric tests. Introduction to least squares and maximum likelihood estimation. Emphasis is on medical applications.
    
    Terms: Autumn, Summer | Units: 3
  • Or EPI 262: Intermediate Biostatistics: Regression, Prediction, Survival Analysis (STATS 262)
    Methods for analyzing longitudinal data. Topics include Kaplan-Meier methods, Cox regression, hazard ratios, time-dependent variables, longitudinal data structures, profile plots, missing data, modeling change, MANOVA, repeated-measures ANOVA, GEE, and mixed models. Emphasis is on practical applications. Prerequisites: basic ANOVA and linear regression.
    
    Terms: Spring | Units: 3
  • Or STATS 202: Statistical Learning and Data Science
    Overview of supervised learning, with a focus on regression and classification methods. Syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines; Some unsupervised learning: principal components and clustering (k-means and hierarchical). Prerequisites: STATS 117, CS 106A, MATH 51, or equivalent. Recommended: STATS 191 or STATS 203. See https://statistics.stanford.edu/course-equiv for equivalent courses in other departments that satisfy these prerequisites.
    
    Terms: Autumn, Spring, Summer | Units: 3
  • Or STATS 256: Modern Statistics for Modern Biology (BIOS 221, STATS 366)
    Application based course in nonparametric statistics. Modern toolbox of visualization and statistical methods for the analysis of data, examples drawn from immunology, microbiology, cancer research and ecology. Methods covered include multivariate methods (PCA and extensions), sparse representations (trees, networks, contingency tables) as well as nonparametric testing (Bootstrap, permutation and Monte Carlo methods). Hands on, use R and cover many Bioconductor packages. Prerequisite: Working knowledge of R and two core Biology courses. Note that the 155 offering is a writing intensive course for undergraduates only and requires instructor consent. (WIM). See https://web.stanford.edu/class/bios221/index.html
    
    Terms: Autumn, Spring | Units: 3
  • Or STATS 261: Intermediate Biostatistics: Analysis of Discrete Data (EPI 261, BIOMEDIN 233)
    Methods for analyzing data from case-control and cross-sectional studies: the 2x2 table, chi-square test, Fisher's exact test, odds ratios, Mantel-Haenzel methods, stratification, tests for matched data, logistic regression, conditional logistic regression. Emphasis is on data analysis in SAS or R. Special topics: cross-fold validation and bootstrap inference.
    
    Terms: Winter | Units: 3
• IMMUNOL 201:  Advanced Immunology I
  For graduate students, medical students and undergraduates. Topics include the innate and adaptive immune systems; genetics and function of immune cells and molecules; lymphocyte activation and regulation of immune responses. Recommended: undergraduate course in immunology.
  
  Terms: Winter | Units: 3
• IMMUNOL 202: Advanced Immunology II
  Readings of immunological literature. Classic problems and emerging areas based on primary literature. Student and faculty presentations. Prerequisite: IMMUNOL 201/MI 211.
  
  Terms: Spring | Units: 3
  
• IMMUNOL 258: Ethics, Science, and Society
  This discussion focused Ethics, Science, and Society interactive mini-course will engage Immunology graduate students, postdoctoral fellows, and faculty in learning and conversations on topics in responsible research (including animal subjects, authorship, collaboration, conflicts of interest, data management, human subjects, mentor-mentee relationships, peer review, publication, research misconduct, and social responsibility) and diversity in science, informed by readings, case studies, individual reflections, and more. Some of the driving themes in this course include: what it means to do research well and how to and not to achieve this, why doing research well and with integrity is important, and who are researchers currently and who should they be. Prerequisite: MED 255
  
  Terms: Spring | Units: 1
• IMMUNOL 290: Teaching in Immunology
  Practical experience in teaching by serving as a teaching assistant in an immunology course. Unit values are allotted individually to reflect the level of teaching responsibility assigned to the student. May be repeated for credit.
  
  Terms: Autumn, Winter, Spring, Summer | Units: 1-18
• IMMUNOL 305: Immunology Journal Club
  Required of first- to third-year graduate students. Graduate students present and discuss recent papers in the literature. May be repeated for credit.
  
  Terms: Autumn, Winter, Spring | Units: 1
  
• IMMUNOL 311: Seminar in Immunology
  Enrollment limited to Ph.D., M.D./Ph.D., and medical students whose scholarly concentrations are in Immunology. Current research topics.
  
  Terms: Autumn, Winter, Spring | Units: 1
• IMMUNOL 399: Graduate Research
  For Ph.D., M.D./Ph.D. students, and medical students whose scholarly concentrations are in Immunology.
  
  Terms: Autumn, Winter, Spring, Summer | Units: 1-18
• MED 255: The Responsible Conduct of Research
  Forum. How to identify and approach ethical dilemmas that commonly arise in biomedical research. Issues in the practice of research such as in publication and interpretation of data, and issues raised by academic/industry ties. Contemporary debates at the interface of biomedical science and society regarding research on stem cells, bioweapons, genetic testing, human subjects, and vertebrate animals. Completion fulfills NIH/ADAMHA requirement for instruction in the ethical conduct of research. Prerequisite: research experience recommended. Intensive format, 1-day course, register for only one section. One pre-class assignment required.
  
  Terms: Autumn, Winter, Spring, Summer | Units: 1
•  

• In addition to the core courses listed above, MCTI first-year students are required to take the following course in their first year for a letter grade:
• IMMUNOL 203: Advanced Immunology III
  Key experiments and papers in immunology. Course focuses on the history of Immunology and how current research fits into the historical context. Students work on developing effective presentation skills.
  
  Terms: Sum | Units: 3

• Two electives (Examples of electives are below. Other courses may be considered to fulfill the elective requirement but approval of the Director must be obtained before enrolling)
• BIO 214: Advanced Cell BIology (MCP 221, BIOC 224)
  For Ph.D. students. Taught from the current literature on cell structure, function, and dynamics. Topics include complex cell phenomena such as cell division, apoptosis, signaling, compartmentalization, transport and trafficking, motility and adhesion, and differentiation. Weekly reading of current papers from the primary literature. Advanced undergraduates may participate with the permission of the Course Director.
  
  Terms: Winter | Units: 3
• BIO 246: Synthetic proteins and genetic circuits (BIOE 266, GENE 246)
  Synthetic proteins and gene circuits are rapidly evolving technologies that are increasingly central to research and medicine. These proteins and gene circuits are core to next-generation medicines as biologics and cell therapies, research tools that give us unprecedented control over biological processes, and serve as powerful industrial tools. Through lecture and discussion of literature, we will explore key concepts including modularity in synthetic biology, methods of protein and circuit design, and practical applications. We will also discuss how directed evolution, high-throughput screening, and machine learning/artificial intelligence might reshape the landscape of synthetic proteins and gene circuits.
  
  Terms: Autumn | Units 2-3
• CBIO 240: Molecular and Genetic Basis of Cancer
  Required for first-year Cancer Biology graduate students. Focus is on fundamental concepts in the molecular biology of cancer, including oncogenes, tumor suppressor genes, and cellular signaling pathways. Emphasis will be given to seminal discoveries and key experiments in the field of cancer molecular biology. Course consists of two 1 hour lectures and one 2 hour discussion per week. Enrollment of undergraduates requires consent of the course director.
  
  Terms: Autumn | Units: 4
• CSB 288: Systems Biology: Principles of Cell Signaling (BIO 188, BIO 288)
  The systems biology set of courses aims to give students an overview of how cells process information to build and replicate themselves as well as respond to extracellular signals and environmental changes. The techniques used and discussed in detail are those currently utilized in modern quantitative cell biology. This course in the systems biology set aims to provide an understanding of the principles of cell signaling as applied to natural and synthetic biological circuits. As a primary example of naturally occurring signaling circuits, we will consider in detail the pathway responsible for controlling cell division in response to intra- and extra-cellular signals. The class will cover classic and current techniques for the genetic analysis of the key regulatory circuits governing the control of cell division. Specific topics include tractable model organisms; growth control; and irreversible biochemical switches. The class will be based on a weekly lecture followed by the analysis of classic and current primary literature as well as basic concepts in nonlinear dynamics.
  
  Terms: Autumn | Units: 3
• DBIO 210: Developmental Biology
  Current areas of research in developmental biology. How organismic complexity is generated during embryonic and post-embryonic development. The roles of genetic networks, gene regulation ,organogenesis, tissue patterning, cell lineage, maternal inheritance, cell-cell communication, signaling, and regeneration in developmental processes in well- studied organisms such as vertebrates, insects, and nematodes. Team-taught. Students meet with faculty to discuss current papers from the literature. Prerequisite: graduate standing, consent of instructor. Recommended: familiarity with basic techniques and experimental rationales of molecular biology, biochemistry, and genetics.
  
  Terms: Spring | Units: 4
• Immunol 206: Introduction to Applied Computational Tools in Immunology
  Introduction to computational tools for analyses of immunological data sets, including but not limited to single-cell data such as that from flow cytometry or CyTOF, Luminex, and genomic analyses. Students become familiar with major web-based databases and analysis suites for immunological and genomic data; gain a working knowledge of the major software/algorithms for working with major data types, and be able to apply at least one computational tool in these areas to analyze a public data set. Lectures will be followed by a demonstration and interaction session on the topic. Students will complete a computational analysis project and present it to the class.
  
  Terms: Winter | Units: 2
• IMMUNOL 223: Biology and Disease of Hematopoiesis (STEMREM 223)
  Hematopoiesis is the formation, development, and differentiation of blood cells. Lecture and journal club. Topics will include definitive and adult hematopoiesis, myeloid and lymphoid development, hematopoietic diseases, stem cell niche, bone marrow transplant, and methods and models used to study hematopoiesis. For upper level undergraduates or graduate students. Pre-requisite for undergraduates: Biology or Human Biology core, or consent of instructor.
  
  Terms: Winter | Units: 3
  
• IMMUNOL 275: Tumor Immunology
  Tumor Immunology focuses on the mechanisms by which tumors can escape from and subvert the immune system and conversely on the ability of innate and adaptive arms of the immune system to recognize and eliminate tumors. Topics include: tumor antigens, tumor immunosurveillance and immunoediting, tumor microenvironment, tumor iniduced immunosuppression, tumorimmunotherapy (including cancer vaccines, CARs, TILs, checkpoint antibodies, monoclonal antibodies and bispecific antibodies, as well as bone marrow transplantation and radiation therapy). Tracks the historical development of our understanding of modulating tumor immune response and discusses their relative significance in the light of current research findings. Prerequisite: for undergraduates, human biology or biology core.
  
  Terms: Spring | Units: 3
  
• MI 210: Advanced Pathogenesis of Bacteria, Viruses, and Eukaryotic Parasites
  For graduate and medical students, and advanced undergraduates; required of first-year graduate students in Microbiology and Immunology. The molecular mechanisms by which microorganisms invade animal and human hosts, express their genomes, interact with macromolecular pathways in the infected host, and induce disease. Current literature. Undergraduate students interested in taking this class must meet with the instructor to obtain approval before enrolling.
  
  Terms: Winter | Units: 4
• SBIO 241: Biological Macromolecules
  The physical and chemical basis of macromolecular function. Topics include: forces that stabilize macromolecular structure and their complexes; thermodynamics and statistical mechanics of macromolecular folding, binding, and allostery; diffusional processes; kinetics of enzymatic processes; the relationship of these principles to practical application in experimental design and interpretation. The class emphasizes interactive learning, and is divided among lectures, in-class group problem solving, and discussion of current and classical literature. Enrollment limited to 30. Prerequisites: Background in biochemistry and physical chemistry recommended but material available for those with deficiency in these areas; undergraduates with consent of instructor only.
  
  Terms: Autumn | Units: 3-5
  
  
•  

• Students in the CSI track are required to take the following core courses in their first and second years, unless demonstrated by proficiency or coursework. For example, a student, with proficiency in concepts taught in CS 106A, may petition to be exempt from this course and go on to take CS 106B. Petitions to be granted an exemption from the courses CS 106A, CS 109, and CS 161 must be approved by one of the Co-Chairs of the CSI Track and the Director of Immunology in advance; exemptions cannot be granted retroactively.
• BIOMEDIN 214: Representations and Algorithms for Computational Molecular Biology (BIOE 214, CS 274, GENE 214)
  Topics: This is a graduate level introduction to bioinformatics and computational biology, algorithms for alignment of biological sequences and structures, computing with strings, phylogenetic tree construction, hidden Markov models, basic structural computations on proteins, protein structure prediction, molecular dynamics and energy minimization, statistical analysis of 3D biological data, integration of data sources, knowledge representation and controlled terminologies for molecular biology, microarray analysis, chemoinformatics, pharmacogenetics, network biology. Note: For Fall 2021, Dr. Altman will be away on sabbatical and so class will be taught from lecture videos recorded in fall of 2018. The class will be entirely online, with no scheduled meeting times. Lectures will be released in batches to encourage pacing. A team of TAs will manage all class logistics and grading. Firm prerequisite: CS 106B.
  
  Terms: Autumn | Units: 3-4
  
• CS 106A: Programming Methodology
  Introduction to the engineering of computer applications emphasizing modern software engineering principles: program design, decomposition, encapsulation, abstraction, and testing. Emphasis is on good programming style and the built-in facilities of respective languages. Uses the Python programming language. No prior programming experience required.
  
  Terms: Autum, Winter, Spring, Summer | Units: 3-5
• CS 106B: Program Abstractions
  Abstraction and its relation to programming. Software engineering principles of data abstraction and modularity. Object-oriented programming, fundamental data structures (such as stacks, queues, sets) and data-directed design. Recursion and recursive data structures (linked lists, trees, graphs). Introduction to time and space complexity analysis. Uses the programming language C++ covering its basic facilities. Prerequisite: 106A or equivalent.
  
  Terms: Autumn, Winter, Spring, Summer | Units: 3-5
• CS 109: Introduction to Probability for Computer Scientists
  Topics include: counting and combinatorics, random variables, conditional probability, independence, distributions, expectation, point estimation, and limit theorems. Applications of probability in computer science including machine learning and the use of probability in the analysis of algorithms. Prerequisites: 103, 106B or X, multivariate calculus at the level of MATH 51 or CME 100 or equivalent.
  
  Terms: Aut, Win, Spr, Sum | Units: 3-5
  
• CS 161: Design and Analysis of Algorithms
  Worst and average case analysis. Recurrences and asymptotics. Efficient algorithms for sorting, searching, and selection. Data structures: binary search trees, heaps, hash tables. Algorithm design techniques: divide-and-conquer, dynamic programming, greedy algorithms, amortized analysis, randomization. Algorithms for fundamental graph problems: minimum-cost spanning tree, connected components, topological sort, and shortest paths. Possible additional topics: network flow, string searching. Prerequisite: 106B or 106X; 103 or 103B; 109 or STATS 116.
  
  Terms: Autumn, Spring, Summer | Units: 3-5
  
  
• IMMUNOL 207: Essential Methods in Computational and Systems Immunology
  Introduction to the major underpinnings of systems immunology: first principles of development of computational approaches to immunological questions and research; details of the algorithms and statistical principles underlying commonly used tools; aspects of study design and analysis of data sets. Prerequisites: CS106a and CS161 strongly recommended.
  
  Terms: Spring | Units: 3
• IMMUNOL 312: Emerging Topics in Computational Immunology
  This course will take an emerging topic of area of interest in computational immunology and give the class some time to discuss and take a hands-on approach with the material . The course will be a mix of talks and hands-on work/projects with a curriculum shaped by recent activities in the field.
  
  Terms: Summer | Units: 1
•  

• Two electives (Examples of electives are below, but are not limited to those listed). If a student chooses to do an elective that is not in the list below, they must ensure it is primarily a computational course.
• BIOMEDIN 212: Introduction to Biomedical Informatics Research Methodology (CS 272, GENE 212, BIOE 212)
  Capstone Biomedical Data Science experience. Hands-on software building. Student teams conceive, design, specify, implement, evaluate, and report on a software project in the domain of biomedicine. Creating written proposals, peer review, providing status reports, and preparing final reports. Issues related to research reproducibility. Guest lectures from professional biomedical informatics systems builders on issues related to the process of project management. Software engineering basics. Because the team projects start in the first week of class, attendance that week is strongly recommended. Prerequisites: BIOMEDIN 210 or 214 or 215 or 217 or 260. Preference to BMI graduate students. Consent of instructor required. NOTE: For students in the Department of Biomedical Data Science Program, this core course MUST be taken as a letter grade only.
  
  Terms: Spring | Units: 3-5
• BIOMEDIN 217: Translational Bioinformatics (GENE 217, CS 275, BIOE 217) 
  Analytic and interpretive methods to optimize the transformation of genetic, genomic, and biological data into diagnostics and therapeutics for medicine. Topics: access and utility of publicly available data sources; types of genome-scale measurements in molecular biology and genomic medicine; linking genome-scale data to clinical data and phenotypes; and new questions in biomedicine using bioinformatics. Case studies. Prerequisites: programming ability at the level of CS 106A and familiarity with statistics and biology.
  
  Terms: Winter, Spring | Units: 3-4
• BIOMEDIN 260: Computational Methods for Biomedical Image Analysis and Interpretation (CS 235, RAD 260, BMP 260)
  The latest biological and medical imaging modalities and their applications in research and medicine. Focus is on computational analytic and interpretive approaches to optimize extraction and use of biological and clinical imaging data for diagnostic and therapeutic translational medical applications. Topics include major image databases, fundamental methods in image processing and quantitative extraction of image features, structured recording of image information including semantic features and ontologies, indexing, search and content-based image retrieval. Case studies include linking image data to genomic, phenotypic and clinical data, developing representations of image phenotypes for use in medical decision support and research applications and the role that biomedical imaging informatics plays in new questions in biomedical science. Includes a project. Enrollment for 3 units requires instructor consent. Prerequisites: programming ability at the level of CS 106A, familiarity with statistics, basic biology. Knowledge of Matlab or Python highly recommended.
  
  Terms: Spring | Units: 3-4
• CME 206: Introduction to Numerical Methods for Engineering (ME 300C)
  Numerical methods from a user's point of view. Lagrange interpolation, splines. Integration: trapezoid, Romberg, Gauss, adaptive quadrature; numerical solution of ordinary differential equations: explicit and implicit methods, multistep methods, Runge-Kutta and predictor-corrector methods, boundary value problems, eigenvalue problems; systems of differential equations, stiffness. Emphasis is on analysis of numerical methods for accuracy, stability, and convergence. Introduction to numerical solutions of partial differential equations; Von Neumann stability analysis; alternating direction implicit methods and nonlinear equations. Prerequisites: CME 200/ME 300A, CME 204/ME 300B.
  
  Terms: Spring | Units: 3
  
• CME 263: Introduction to Linear Dynamical System (EE 263)
  Applied linear algebra and linear dynamical systems with applications to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular-value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer-matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: Linear algebra and matrices as in ENGR 108 or MATH 104; ordinary differential equations and Laplace transforms as in EE 102B or CME 102.
  
  Terms: Autumn | Units: 3
  
• CME 309:  Randomized Algorithms and Probabilistic Analysis (CS 265)
  Randomness pervades the natural processes around us, from the formation of networks, to genetic recombination, to quantum physics. Randomness is also a powerful tool that can be leveraged to create algorithms and data structures which, in many cases, are more efficient and simpler than their deterministic counterparts. This course covers the key tools of probabilistic analysis, and application of these tools to understand the behaviors of random processes and algorithms. Emphasis is on theoretical foundations, though we will apply this theory broadly, discussing applications in machine learning and data analysis, networking, and systems. Topics include tail bounds, the probabilistic method, Markov chains, and martingales, with applications to analyzing random graphs, metric embeddings, random walks, and a host of powerful and elegant randomized algorithms. Prerequisites: CS 161 and STAT 116, or equivalents and instructor consent.
  
  Terms:  Autumn, Winter | Units:  3
• CME 364A: Convex Optimization I (EE 364A)
  Convex sets, functions, and optimization problems. The basics of convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications. Least-squares, linear and quadratic programs, semidefinite programming, and geometric programming. Numerical algorithms for smooth and equality constrained problems; interior-point methods for inequality constrained problems. Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering. Prerequisite: linear algebra such as EE263, basic probability.
  
  Terms: Winter | Units: 3
• CS 228: Probabilistic Graphical Models: Principles and Techniques
  Probabilistic graphical modeling languages for representing complex domains, algorithms for reasoning using these representations, and learning these representations from data. Topics include: Bayesian and Markov networks, extensions to temporal modeling such as hidden Markov models and dynamic Bayesian networks, exact and approximate probabilistic inference algorithms, and methods for learning models from data. Also included are sample applications to various domains including speech recognition, biological modeling and discovery, medical diagnosis, message encoding, vision, and robot motion planning. Prerequisites: basic probability theory and algorithm design and analysis.
  
  Terms: Winter | Units: 3-4
• CS 229: Machine Learning (STATS 229)
  Topics: statistical pattern recognition, linear and non-linear regression, non-parametric methods, exponential family, GLMs, support vector machines, kernel methods, deep learning, model/feature selection, learning theory, ML advice, clustering, density estimation, EM, dimensionality reduction, ICA, PCA, reinforcement learning and adaptive control, Markov decision processes, approximate dynamic programming, and policy search. Prerequisites: knowledge of basic computer science principles and skills at a level sufficient to write a reasonably non-trivial computer program in Python/NumPy to the equivalency of CS106A, CS106B, or CS106X, familiarity with probability theory to the equivalency of CS 109, MATH151, or STATS 116, and familiarity with multivariable calculus and linear algebra to the equivalency of MATH51 or CS205.
  
  Terms: Autumn, Winter, Summer | Units: 3-4
• CS 231N: Deep Learning for Computer Vision
  Computer Vision has become ubiquitous in our society, with applications in search, image understanding, apps, mapping, medicine, drones, and self-driving cars. Core to many of these applications are visual recognition tasks such as image classification and object detection. Recent developments in neural network approaches have greatly advanced the performance of these state-of-the-art visual recognition systems. This course is a deep dive into details of neural-network based deep learning methods for computer vision. During this course, students will learn to implement, train and debug their own neural networks and gain a detailed understanding of cutting-edge research in computer vision. We will cover learning algorithms, neural network architectures, and practical engineering tricks for training and fine-tuning networks for visual recognition tasks.Prerequisites: Proficiency in Python - All class assignments will be in Python (and use numpy) (we provide a tutorial here for those who aren't as familiar with Python). If you have a lot of programming experience but in a different language (e.g. C/C++/Matlab/Javascript) you will probably be fine.College Calculus, Linear Algebra (e.g. MATH 19, MATH 51) -You should be comfortable taking derivatives and understanding matrix vector operations and notation. Basic Probability and Statistics (e.g. CS 109 or other stats course) -You should know basics of probabilities, gaussian distributions, mean, standard deviation, etc.
  
  Terms: Spring | Units: 3-4
• CS 279 Computational Biology: Structure and Organization of Biomolecules and Cells (BIOMEDIN 279, BIOE 279, CME 279, BIOPHYS 279)
  Computational techniques for investigating and designing the three-dimensional structure and dynamics of biomolecules and cells. These computational methods play an increasingly important role in drug discovery, medicine, bioengineering, and molecular biology. Course topics include protein structure prediction, protein design, drug screening, molecular simulation, cellular-level simulation, image analysis for microscopy, and methods for solving structures from crystallography and electron microscopy data. Prerequisites: elementary programming background (CS 106A or equivalent) and an introductory course in biology or biochemistry.
  
  Terms: Autumn | Units: 3
• CS 372: Artificial Intelligence for Reasoning, Planning, and Decision Making
  Course Description:Large Language Models (LLMs) have revolutionized AI through remarkable pattern matching capabilities. However, the path to Artificial General Intelligence (AGI) requires advancing beyond unconscious (System 1) to conscious (System 2) processing. This research-oriented course explores fundamental approaches to elevate LLMs toward AGI capabilities through conscious reasoning, planning, and decision-making. Core Research Questions: 1. How can we enable LLMs to transition from pattern matching to conscious deliberation? 2. What frameworks support robust reasoning and verifiable decisions? 3. How do we implement planning and temporal awareness in LLM systems? 4. What role does multi-LLM agent collaboration play in advancing toward AGI capabilities? The course examines: 1. Theoretical foundations of consciousness in AI 2. Multi-LLM Agent Collaborative Intelligence (MACI) frameworks 3. Entropy-guided information exchange 4. Constitutional AI principles 5. Temporal reasoning and planning architectures. Through lectures, discussions, and hands-on projects, students will explore practical implementations across various domains. While healthcare provides immediate applications (diagnosis, treatment planning), the principles apply broadly to any field requiring AGI-level reasoning capabilities. Prerequisites: Machine Learning, Deep Learning
  
  Terms: Spring | Units: 3
• EE 276: Information Theory
  (Formerly EE 376A.) Information theory was invented as a mathematical theory for communication but has subsequently found a broad range of applications. We study how to measure, represent, and communicate information effectively: from the foundational concepts of entropy and mutual information to the fundamental role they play in data representation, communication, inference, practical compression and error correction. As time allows, we cover relations and applications to other areas such as probability, statistics, learning and genomics. Prerequisite: a first undergraduate course in probability.
  
  Terms:  Winter | Units: 3
• EE 278: Probability and Statistical Inference
  Many engineering applications require efficient methods to process, analyze, and infer signals, data and models of interest that are best described probabilistically. Building on a first course in probability (such as EE178 or equivalent), this course introduces more advanced topics in probability such as concentration inequalities, random vectors and random processes, and explores their applications in statistics, machine learning and signal processing. Specific applications include hypothesis testing and classification; dimensionality reduction and generalization in machine learning, minimum mean square error estimation and Kalman filtering. Prerequisites: EE178 or equivalent
  
  Terms: Autumn | Units: 3
• STATS 116: Theory of Probability
  Probability spaces as models for phenomena with statistical regularity. Discrete spaces (binomial, hypergeometric, Poisson). Continuous spaces (normal, exponential) and densities. Random variables, expectation, independence, conditional probability. Introduction to the laws of large numbers and central limit theorem. Prerequisites: MATH 52 and familiarity with infinite series, or equivalent. Undergraduate students enroll for 5 units, graduate students enroll for 4 units. Undergraduate students must enroll in one section in addition to the main lecture. Sections are optional for graduate students. Note: Autumn 2023-24 is the last time this course will be offered. It will be replaced by STATS 117 and STATS 118 in 2024-25.
  
  Terms: Autumn | Units: 4-5
• STATS 202: Statistical Learning and Data Science
  Overview of supervised learning, with a focus on regression and classification methods. Syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines; Some unsupervised learning: principal components and clustering (k-means and hierarchical). Prerequisites: STATS 117, CS 106A, MATH 51, or equivalent. Recommended: STATS 191 or STATS 203. See https://statistics.stanford.edu/course-equiv for equivalent courses in other departments that satisfy these prerequisites.
  
  Terms: Spring | Units: 3
  
• STATS 216: Introduction to Statistical Learning
  Overview of supervised learning, with a focus on regression and classification methods. Syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis;cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines; Some unsupervised learning: principal components and clustering (k-means and hierarchical). Computing is done in R, through tutorial sessions and homework assignments. This math-light course is offered via video segments (MOOC style), and in-class problem solving sessions. Prereqs: Introductory courses in statistics or probability (e.g., Stats 60 or Stats 101), linear algebra (e.g., Math 51), and computer programming (e.g., CS 105). May not be taken for credit by students with credit in STATS 202 or STATS 216V.
  
  Terms: Autumn | Units: 3
• STATS 217: Introduction to Stochastic Processes
  Discrete and continuous time Markov chains, Poisson processes, random walks, branching processes, first passage times, recurrence and transience, stationary distributions. Prerequisites: (recommended) STATS 117, MATH 51, MATH 104, or equivalent. See https://statistics.stanford.edu/course-equiv for equivalent courses in other departments that satisfy these prerequisites.
  
  Terms: Winter, Summer | Units: 3
  
• STATS 256: Modern Statistics for Modern Biology (BIOS 221, STATS 366)
  Application based course in nonparametric statistics. Modern toolbox of visualization and statistical methods for the analysis of data, examples drawn from immunology, microbiology, cancer research and ecology. Methods covered include multivariate methods (PCA and extensions), sparse representations (trees, networks, contingency tables) as well as nonparametric testing (Bootstrap, permutation and Monte Carlo methods). Hands on, use R and cover many Bioconductor packages. Prerequisite: Working knowledge of R and two core Biology courses. Note that the 155 offering is a writing intensive course for undergraduates only and requires instructor consent. (WIM). See https://web.stanford.edu/class/bios221/index.html
  
  Terms: Autumn | Units: 3
• STATS 261: Intermediate Biostatistics: Analysis of Discrete Data (EPI 261, BIOMEDIN 233)
  Methods for analyzing data from case-control and cross-sectional studies: the 2x2 table, chi-square test, Fisher's exact test, odds ratios, Mantel-Haenzel methods, stratification, tests for matched data, logistic regression, conditional logistic regression. Emphasis is on data analysis in SAS or R. Special topics: cross-fold validation and bootstrap inference.
  
  Terms: Winter | Units: 3
• STATS 262: Intermediate Biostatistics: Regression, Prediction, Survival Analysis (EPI 262)
  Methods for analyzing longitudinal data. Topics include Kaplan-Meier methods, Cox regression, hazard ratios, time-dependent variables, longitudinal data structures, profile plots, missing data, modeling change, MANOVA, repeated-measures ANOVA, GEE, and mixed models. Emphasis is on practical applications. Prerequisites: basic ANOVA and linear regression.
  
  Terms: Spring | Units: 3
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• BIOS 431: Implement a Writing Practice to Increase your Scientific Productivity
  This course is for graduate students in the biosciences who want to learn about best practices for developing writing skills and a writing routine. The course uses a variety of strategies to engage students in writing such as: lectures, readings, generative discussions, and guest speakers. The course includes dedicated writing time for students to actively apply new strategies. This class is repeatable for credit. New students must enroll for 2-units and returning students are to enroll for 1-unit and attend class only on writing days.
  
  Terms: Autumn, Winter, Spring | Units: 1-2
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